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经济代写|微观经济学代写Microeconomics代考|LONG RUN VERSUS SHORT RUN

We will study the firm’s cost-minimization problem in the long run and in the short run. Although the terms long run and short run seem to connote a length of time, it is more useful to think of them as pertaining to the degree to which the firm faces constraints in its decision-making flexibility. A firm that makes a long run decision faces a blank slate (i.e., no constraints): Over the long run, it will be able to vary the quantities of all its inputs as much as it desires. When our sporting goods firm in the previous section decides whether to build a new bowling ball factory, it faces a long-run decision. It is free to choose whether to build the factory and, if so, how large to make it. As it does this, it can simultaneously choose other input quantities, such as the size of the workforce and the amount of land for the factory. Because the firm can, in principle, avoid the costs of all inputs by choosing not to build, the costs associated with this long-run decision are necessarily nonsunk.

By contrast, a firm facing a short-run decision is subject to constraints: Over the short run, it will not be able to adjust the quantities of some of its inputs and/or reverse the consequences of past decisions that it has made regarding those inputs. For example, once our bowling ball firm builds a factory, it will, at least for a while, face short-run decisions, such as how many workers it should employ given the physical constraints of its capacity.

In microeconomics, the concept of short run and long run is convenient analytical simplifications to help us focus our attention on the interesting features of the problem at hand. In reality, firms face a continuum of “runs”; some decisions involve “blanker slates” than others. In this section, we first focus on long-run cost minimization in order to study carefully the trade-offs that firms can make in input choices when they start with a blank slate. In the next section, we turn to short-run cost minimization to highlight how constraints on input usage can limit the firm’s ability to minimize costs.

经济代写|微观经济学代写Microeconomics代考|THE LONG-RUN COST-MINIMIZATION PROBLEM

The cost-minimization problem is an example of constrained optimization, first discussed in Chapter 1. We want to minimize the firm’s total costs, subject to the requirement that the firm produce a given amount of output. In Chapter 4, we encountered two other examples of constrained optimization: the problem of maximizing utility subject to a budget constraint (utility maximization) and the problem of minimizing consumption expenditures, subject to achieving a minimum level of utility (expenditure minimization). You will see that the cost-minimization problem closely resembles the expenditure-minimization problem from consumer choice theory.

Let’s study the long-run cost-minimization problem for a firm that uses two inputs: labor and capital. Each input has a price. The price of a unit of labor servicesalso called the wage rate-is $w$. This price per unit of capital services is $r$. The price of labor could be either an explicit cost or an implicit cost. It would be an explicit cost if the firm (as most firms do) hires workers in the open market. It would be an implicit cost if the firm’s owner provides her own labor to run the firm and, in so doing, sacrifices outside employment opportunities. Similarly, the price of capital could either be an explicit cost or an implicit cost. It would be an explicit cost if the firm leased capital services from another firm (e.g., a firm that leases computer time on a server to host its website). It would be an implicit cost if the firm owned the physical capital and, by using it in its own business, sacrificed the opportunity to sell capital services to other firms.

The firm has decided to produce $Q_0$ units of output during the next year. In later chapters, we will study how the firm makes such an output decision. For now, the quantity $Q_0$ is exogenous (e.g., as if the manufacturing manager of the firm has been told how much to produce). The long-run cost-minimization problem facing the manufacturing manager is to figure out how to produce that amount in the cost-minimizing way. Thus, the manager must choose a quantity of capital $K$ and a quantity of labor $L$ that minimize the total cost $T C=w L+r K$ of producing $Q_0$ units of output. This total cost is the sum of all the economic costs the firm incurs when it uses labor and capital services to produce output.

经济代写|微观经济学代写Microeconomics代考|ECON20002

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经济代写|微观经济学代写Microeconomics代考|LONG RUN VERSUS SHORT RUN

我们将研究企业在长期和短期内的成本最小化问题。尽管长期和短期这两个术语似乎意味着时间的长度,但将它们视为与公司在决策灵活性方面面临约束的程度有关更有用。做出长期决策的公司面临一张白纸(即没有约束):从长远来看,它将能够随心所欲地改变所有投入的数量。当我们在上一节中的体育用品公司决定是否建立一个新的保龄球工厂时,它面临着一个长期决策。可以自由选择是否建造工厂,如果建造的话,建造的规模有多大。在这样做的同时,它可以同时选择其他投入量,例如劳动力规模和工厂用地数量。

相比之下,面临短期决策的公司受到约束:在短期内,它将无法调整其某些投入的数量和/或扭转其过去就这些投入做出的决策的后果输入。例如,一旦我们的保龄球公司建了一家工厂,至少在一段时间内,它将面临短期决策,例如考虑到其产能的物理限制,它应该雇用多少工人。

在微观经济学中,短期和长期的概念是方便的分析简化,可帮助我们将注意力集中在手头问题的有趣特征上。实际上,公司面临着连续不断的“挤兑”;有些决定比其他决定涉及“白板”。在本节中,我们首先关注长期成本最小化,以便仔细研究企业在从白纸开始时可以在投入选择中做出的权衡。在下一节中,我们转向短期成本最小化,以强调对投入使用的限制如何限制公司最小化成本的能力。

经济代写|微观经济学代写Microeconomics代考|THE LONG-RUN COST-MINIMIZATION PROBLEM

成本最小化问题是第 1 章中首次讨论的约束优化问题。我们希望在满足公司生产给定产量的要求的情况下,使公司的总成本最小化。在第 4 章中,我们遇到了另外两个约束优化的例子:在预算约束下最大化效用的问题(效用最大化)和在实现最低效用水平的情况下最小化消费支出的问题(支出最小化)。您会发现成本最小化问题与消费者选择理论中的支出最小化问题非常相似。

让我们研究使用两种投入(劳动力和资本)的公司的长期成本最小化问题。每个输入都有一个价格。一单位劳务的价格也称为工资率——是在. 每单位资本服务的价格是r. 劳动力价格可以是显性成本,也可以是隐性成本。如果公司(像大多数公司那样)在公开市场上雇用工人,这将是一项显性成本。如果公司所有者提供自己的劳动力来经营公司,并且在这样做的过程中牺牲了外部就业机会,这将是隐性成本。同样,资本价格可以是显性成本,也可以是隐性成本。如果公司从另一家公司租赁资本服务(例如,一家公司租用服务器上的计算机时间来托管其网站),这将是一项显性成本。如果公司拥有实物资本并在自己的业务中使用它,从而牺牲了向其他公司出售资本服务的机会,那么这将是隐性成本。

公司决定生产问0下一年的产出单位。在后面的章节中,我们将研究企业如何做出这样的产出决策。目前,数量问0是外生的(例如,好像公司的制造经理已被告知要生产多少)。制造经理面临的长期成本最小化问题是找出如何以成本最小化的方式生产该数量的产品。因此,经理必须选择一定数量的资本钾和一定的劳动量大号使总成本最小化吨C=在大号+r钾生产的问0输出单位。该总成本是企业在使用劳动力和资本服务生产产出时所产生的所有经济成本的总和。

经济代写|微观经济学代写Microeconomics代考

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